Kindly explain me this solution in detail

I have attached the three questions. I will be highly greatful if anyone of you explain me these solutions in Detail. Thaks a lot

Attachment 12939

Attachment 12940

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- Sep 17th 2009, 05:02 AMmoonnightingalekindly explain me solution of integration
Kindly explain me this solution in detail

I have attached the three questions. I will be highly greatful if anyone of you explain me these solutions in Detail. Thaks a lot

Attachment 12939

Attachment 12940 - Sep 17th 2009, 06:29 AMCaptainBlack
$\displaystyle \cos^2(2 \pi f_0 t) = (\cos(4 \pi f_0 t)+1)/2$

then as $\displaystyle \cos$ is symetrical in all sorts of ways the right hand side will integrate up to half the area eonclosed in the rectangle enclosing the curve, which has height $\displaystyle 1$ and length $\displaystyle T_0$.

(Draw a picture of the curve, it will then be obvious)

CB - Sep 17th 2009, 06:32 AMCaptainBlack